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Abstract and Applied Analysis
Volume 2014, Article ID 816473, 9 pages
Research Article

A Pseudospectral Algorithm for Solving Multipantograph Delay Systems on a Semi-Infinite Interval Using Legendre Rational Functions

1Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
2Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3Department of Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey
4Institute of Space Sciences, 76900 Magurele-Buchaarest, Romania
5Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
6Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef 62511, Egypt
7Department of Basic Science, Institute of Information Technology, Modern Academy, Cairo 11931, Egypt

Received 26 December 2013; Accepted 25 April 2014; Published 19 May 2014

Academic Editor: Robert A. Van Gorder

Copyright © 2014 E. H. Doha et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new Legendre rational pseudospectral scheme is proposed and developed for solving numerically systems of linear and nonlinear multipantograph equations on a semi-infinite interval. A Legendre rational collocation method based on Legendre rational-Gauss quadrature points is utilized to reduce the solution of such systems to systems of linear and nonlinear algebraic equations. In addition, accurate approximations are achieved by selecting few Legendre rational-Gauss collocation points. The numerical results obtained by this method have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively limited nodes used, the absolute error in our numerical solutions is sufficiently small.